Your experiment shouldn't need to presume the coin is fair. Flipping an unfair coin twice in a row and discarding the HH and TT doubles will generate close to

Your experiment shouldn't need to presume the coin is fair. Flipping an unfair coin twice in a row and discarding the HH and TT doubles will generate close to 50% HT pairs and 50% TH pairs. This only presumes that subsequent flips are independent events. It's still not going to be exactly 50%, because random events are random. You can get as small an error margin as you need by increasing the number of trials. And in some cases, this property of statistical analysis makes it easier to increase N than reduce the randomness and uncertainty in the experiment.